How Can You Factor the Trigonometric Expression sin^3(x)-cos^3(x)?

In summary, Trigonometric identities are mathematical equations that involve trigonometric functions and are used to relate and simplify expressions. It is important to verify these identities to ensure accuracy and validity in mathematical equations. This can be done by manipulating the equation using algebraic techniques and trigonometric properties. Some common strategies include using Pythagorean, sum and difference, double angle, and half angle identities. Success tips include starting with the more complex side, using multiple identities, substituting identities, and being familiar with common trigonometric identities.
  • #1
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Homework Statement



sin^3(x)-cos^3(x)
sin(x) - cos(x)

equals

1 + sin(x) + cos(x)

Homework Equations


Not sure :/


The Attempt at a Solution


Not sure where to even start.
 
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  • #2
Are you sure that it's 1+sin(x)+cos(x) and not 1+sin(x)cos(x)?

Use the identity sin^2(x)+cos^2(x)=1.
 
  • #3
Oh yeah, that was it.
 
  • #4
sin^3(x)-cos^3(x)
-----------------
sin(x) - cos(x)

Try factoring the numerator, it may help you.
 

Related to How Can You Factor the Trigonometric Expression sin^3(x)-cos^3(x)?

What are trigonometric identities?

Trigonometric identities are mathematical equations that involve trigonometric functions such as sine, cosine, and tangent. They are used to relate the values of these functions to each other and to simplify complex expressions.

Why is it important to verify trigonometric identities?

Verifying trigonometric identities is important because it ensures the accuracy and validity of mathematical equations involving trigonometric functions. It also helps in simplifying complex expressions and solving trigonometric equations.

How do you verify a trigonometric identity?

To verify a trigonometric identity, you need to manipulate the equation using algebraic techniques and the properties of trigonometric functions. This involves simplifying both sides of the equation and showing that they are equal to each other.

What are the common strategies used to verify trigonometric identities?

Some common strategies used to verify trigonometric identities include using the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities. It is also helpful to convert all trigonometric functions to sine and cosine.

What are some tips for successfully verifying trigonometric identities?

Some tips for successfully verifying trigonometric identities include starting with the more complex side of the equation, using multiple identities in one step, substituting identities for expressions, and being familiar with common trigonometric identities.

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